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In this paper we give an analytic tableau calculus P L 1 6 for a functionally complete extension of Shramko and Wansing’s logic. The calculus is based on signed formulas and a single set of tableau rules is involved in axiomatising each of the four entailment relations ⊧ t, ⊧ f, ⊧ i, and ⊧ under consideration—the differences only residing in initial assignments of signs to formulas. Proving that two sets of formulas are in one of the first three entailment (...) 

Antirealistic conceptions of truth and falsity are usually epistemic or inferentialist. Truth is regarded as knowability, or provability, or warranted assertability, and the falsity of a statement or formula is identified with the truth of its negation. In this paper, a noninferentialist but nevertheless antirealistic conception of logical truth and falsity is developed. According to this conception, a formula (or a declarative sentence) A is logically true if and only if no matter what is told about what is told about (...) 



Sequent calculi for trilattice logics, including those that are determined by the truth entailment, the falsity entailment and their intersection, are given. This partly answers the problems in ShramkoWansing. 

A sequent calculus for Odintsov’s Hilbertstyle axiomatization of a logic related to the trilattice SIXTEEN3 of generalized truth values is introduced. The completeness theorem w.r.t. a simple semantics for is proved using Maehara’s decomposition method that simultaneously derives the cutelimination theorem for . A firstorder extension of and its semantics are also introduced. The completeness and cutelimination theorems for are proved using Schütte’s method. 

